Spontaneous potential (SP) well-logging is one of the most common and
useful well-logging techniques in petroleum exploitation. This monograph
is the first of its kind on the mathematical model of spontaneous
potential well-logging and its numerical solutions. The mathematical
model established in this book shows the necessity of introducing
Sobolev spaces with fractional power, which seriously increases the
difficulty of proving the well-posedness and proposing numerical
solution schemes. In this book, in the axisymmetric situation the
well-posedness of the corresponding mathematical model is proved and
three efficient schemes of numerical solution are proposed, supported by
a number of numerical examples to meet practical computation needs.